Without multiplying anything out, decide which of these products is NEGATIVE.

Class 7Rational NumbersRational Numbers

A $\frac{- 3}{4} \times \frac{- 5}{7}$
B $\frac{2}{- 5} \times \frac{3}{8}$
C $\frac{- 1}{2} \times \frac{- 1}{2}$
D $\frac{- 6}{- 7} \times \frac{5}{9}$

Step-by-Step Solution

Judge each factor's sign first.

\frac{2}{- 5} = \frac{- 2}{5}

is negative and

\frac{3}{8}

is positive, so this product is negative. The first and third are negative × negative = positive, and

\frac{- 6}{- 7} = \frac{6}{7}

is positive, so the last is positive × positive. Counting visible minus signs instead of reading each factor's true sign is what goes wrong here.

Answer: B)

\frac{2}{- 5} \times \frac{3}{8}

Key idea: Recognising rationals

If you can write a number as **integer over non-zero integer**, it is rational. So:

- All integers are rational: 5 = 5/1, 0 = 0/1, −9 = −9/1.
- All fractions with integer numerator and denominator are rational: 3/4, −2/7, 11/3.
- Any decimal that terminates or repeats is rational: 0.25 = 1/4, 0.333… = 1/3.

Numbers that cannot be written as p/q (like √2 or π) are NOT rational — they're irrational. You'll meet those in Class 9.

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